Electromagnetic Induction Chapter-Wise Test 18

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil of 200 turns is placed in a field that decreases from 0.05 T to 0 in 0.4 s. If the area is 0.02 m², what is the induced emf?

\( \Delta \Phi = B A = 0.05 \times 0.02 = 0.001 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 200 \times \frac{0.001}{0.4} = 0.5 \, \text{V} \).

0.3 V
0.4 V
0.5 V
0.6 V
3

A coil is placed near a current-carrying wire. If the current in the wire is suddenly switched off, what happens to the magnetic flux through the coil?

When the current is switched off, the magnetic field due to the wire collapses, reducing the magnetic flux through the coil from some value to zero.

Increases
Decreases
Remains constant
Becomes infinite
1

A coil of 150 turns and area 0.01 m² is rotated at 40 Hz in a 0.06 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 40 = 80\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 150 \times 0.06 \times 0.01 \times 80\pi = 22.62 \, \text{V} \).

20 V
21 V
22 V
22.62 V
4

A conducting loop is twisted in a uniform magnetic field. The induced emf arises primarily from what change?

Twisting changes the orientation of the loop’s area vector relative to the field, altering the magnetic flux and inducing an emf.

Increase in field strength
Decrease in loop size
Change in flux due to orientation
Change in loop resistance
3

A coil of 50 turns has an area of 0.03 m² in a 0.2 T field. If the field drops to zero in 0.1 s, what is the induced emf?

\( \Delta \Phi = B A = 0.2 \times 0.03 = 0.006 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 50 \times \frac{0.006}{0.1} = 3 \, \text{V} \).

1.5 V
2 V
3 V
4 V
3

A rod of length 0.6 m moves at 2.5 m/s in a 0.25 T field perpendicular to its length. What is the induced emf?

\( \varepsilon = B l v = 0.25 \times 0.6 \times 2.5 = 0.375 \, \text{V} \).

0.375 V
0.4 V
0.45 V
0.5 V
1

A solenoid of 600 turns and length 0.8 m induces an emf of 2 V in a nearby coil when its current changes from 1 A to 4 A in 0.2 s. What is the mutual inductance?

\( \varepsilon = M \frac{\Delta I}{\Delta t} \).

\( \Delta I = 4 - 1 = 3 \, \text{A} \), \( \Delta t = 0.2 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{2}{\frac{3}{0.2}} = \frac{2}{15} = 0.133 \, \text{H} \approx 0.13 \, \text{H} \).

0.13 H
0.15 H
0.18 H
0.2 H
1

A rod rotates at 25 rad/s in a 0.3 T field. If the length from the axis to the tip is 0.8 m, what is the emf induced?

\( \varepsilon = \frac{1}{2} B \omega R^2 \).

\( \varepsilon = \frac{1}{2} \times 0.3 \times 25 \times (0.8)^2 = 2.4 \, \text{V} \).

2.0 V
2.2 V
2.4 V
2.6 V
3

A loop of 0.3 m × 0.12 m moves out of a 0.4 T field at 2 m/s along its longer side. How long does the emf last?

Time = distance/velocity, distance = width along motion = 0.12 m.

\( t = \frac{0.12}{2} = 0.06 \, \text{s} \).

0.03 s
0.05 s
0.06 s
0.08 s
3

A wheel with 6 spokes of 0.6 m each rotates at 45 rpm in a 0.5 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{45}{60} = 1.5\pi \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.5 \times 1.5\pi \times (0.6)^2 = 0.8478 \, \text{V} \approx 0.85 \, \text{V} \).

0.7 V
0.75 V
0.8 V
0.85 V
4

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